The complexity of the industry and your own knowledge of the industry will dictate the need for 3rd party operational due diligence. The most important advice I can give in this case is that you not treat this as a 3rd party exercise where you get the report and review it. You should participate/be present in the meetings/sessions with the consultants/experts. this is an incredible opportunity to learn about the industry, the company and the team.

The answer will be very specific to a sector/company you are looking at. At a minimum, you will need to understand what are the key processes/KPIs/measures of success in a given sector, source corresponding benchmarks, and understand how your target compares to these benchmarks (i.e., market leader vs. laggard) and why (root cause analysis). That will then help you with (1) deciding if the company is of interest - some will be comfortable buying company requiring a transformation, others wont (2) decide how much you are willing to pay - the quality of operations and amount of work required to improve the business should inform price negotiations (3) draft the value creation plan - the plan should aim to get you to perform better on the benchmarks, (4) measure progress.

If that's available to you, speaking with industry experts/brokers/riverguides will most likely get you there fastest.

I also previously used APQC to understand key processes, measures and benchmarks across multitude of industries. That can be a good place to start but is not free.